According to Moseley.s law, the frequency of a spectral line in X-ray spectrum varies as

Options

A. Atomic number of element
B. Square of atomic number of element
C. Square root of atomic number of element
D. Fourth power of atomic number of element

Answer

To solve the question regarding Moseley's law and how the frequency of a spectral line in the X-ray spectrum varies, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Moseley's Law**: Moseley's law states that the frequency (ν) of the X-ray spectral lines is related to the atomic number (Z) of the element. The mathematical expression for Moseley's law is given by:
\[ \sqrt{\nu} = A(Z - B) \]
where A and B are constants specific to the type of X-ray line.

2. **Squaring Both Sides**: To eliminate the square root, we square both sides of the equation:
\[ \nu = A^2(Z - B)^2 \]

3. **Neglecting B for High Atomic Numbers**: For elements with a high atomic number (Z), the term B becomes negligible compared to Z. Thus, we can simplify the equation:
\[ \nu \approx A^2(Z^2) \]

4. **Identifying the Relationship**: From the simplified equation, we can see that the frequency (ν) is directly proportional to the square of the atomic number (Z):
\[ \nu \propto Z^2 \]

5. **Conclusion**: Therefore, according to Moseley's law, the frequency of a spectral line in the X-ray spectrum varies as the square of the atomic number of the element.

### Final Answer:
The correct option is that the frequency of a spectral line in the X-ray spectrum varies as \( Z^2 \).

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